Some notes on ergodic theorem for U-statistics of order m for stationary and not necessarily ergodic sequences

2023/09/12 by Davide Giraudo, Giraudo, Davide
Decision Sciences · Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Probability and Risk Models #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2309.05988

openalex publication_date 2023/09/12 · openalex created_date 2023/09/14 · openalex updated_date 2026/08/01

Abstract

In this note, we give sufficient conditions for the almost sure and the convergence in \mathbbL^p of a U-statistic of order m built on a strictly stationary but not necessarily ergodic sequence.

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